The woman arrived at the Royal Free Hospital in north London on Tuesday. She was transferred from Glasgow on a military plane in a quarantine tent.
She had arrived in Britain on Sunday night from Sierra Leone and became ill Monday morning. Officials say she is the first patient diagnosed with Ebola inside Britain.
Her condition is described as "stable" and she is said to be in the early stages of the disease.
The woman had worked with Save the Children in Sierra Leone helping people with the often-fatal disease.
Officials say the risk to the public in Britain is extremely low, but they are tracing passengers who traveled with the patient on her journey home via Casablanca and London's Heathrow Airport.
Paul Cosford, director for health protection for Public Health England, said the passengers were being contacted "on a very precautionary basis."
"But I would emphasize the risk is extremely low to anybody else outside of the hospital treating her," he told the BBC.
The only previous victim of the often-fatal disease in Britain was William Pooley, a nurse who contracted the disease while treating patients in Sierra Leone. He recovered after treatment in London and returned to West Africa.
Since an Ebola outbreak began in December 2013 in the West African country of Guinea, there have been more than 20,000 cases and more than 7,800 deaths, mostly in Liberia, Guinea and Sierra Leone.
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